PHASER: A Universal Simulator for Dynamical Systems

在过去的二十年里，通过采用数值模拟和科学可视化，微分方程及其应用的本科生课程经历了革命性的变化。几个著名的商业软件产品，包括1989年EDUCOM/NCRIPTAL“高等教育最佳数学软件”奖的获得者Phaser，使这场革命成为可能。最初的Phaser已经完全用Java重写了，Java是一种平台中立的语言，具有出色的互联网支持。添加了许多新的可视化功能，特别是用于查看和组织多个模拟的图库。该项目支持Phaser的三个全面开发活动：(A)开发和免费分发Phaser的浏览器版本，类似于Adobe的AcroBatReader；促进在互联网上广泛分发动态Phaser项目和库。(B)与数学家、科学家和工程师合作，创建多学科微分和差分方程式项目的门户，将这些项目发布在www.phaser.com上，并创建适用于初学者和高级本科生的动力系统及其应用库。(C)与不同机构的学生和教职员工测试和评估Phaser的使用。此外，Phaser数值引擎的开发仍在继续。正在开发和测试方法，以验证使用阴影概念的混沌系统的数值模拟。

In past two decades, undergraduate courses in differential equations and their applications have undergone revolutionary changes by embracing numerical simulations and scientific visualization. Several notable commercial software products, including Phaser, the winner of EDUCOM/NCRIPTAL "Best Mathematics Software in Higher Education" award in 1989, have made this revolution possible. The original Phaser has been completely rewritten in Java, a platform-neutral language with excellent Internet support. Many new visualization features have been added, notably a Gallery for viewing and organizing multiple simulations. This project is supporting three full-scale development activities for Phaser:(a) Developing and distributing freely a browser version of Phaser, akin to AcrobatReader by Adobe; and facilitating wide distribution of dynamic Phaser Projects and Galleries over the Internet.(b) Creating a portal of multidisciplinary differential and difference equationsprojects in collaboration with mathematicians, scientists, and engineers, posting these projects on www.phaser.com, and creating Galleries for dynamical systems and their applications suitable for beginning and advanced undergraduate students.(c) Testing and evaluating the use of Phaser with students and faculty at diverse institutions.In addition, development continues on the Phaser numerical engine. Methods are being developed and tested for validating numerical simulations of chaotic systems using the concept of shadowing.